Approximation Theorems for Generalized Complex Kantorovich-Type Operators

Abstract

The order of simultaneous approximation and Voronovskaja-type results with quantitative estimate for complex q-Kantorovich polynomials ($q>0$) attached to analytic functions on compact disks are obtained. In particular, it is proved that for functions analytic in , $R>q$, the rate of approximation by the q-Kantorovich operators ($q>1$) is of order $q^{-n}$ versus $1/n$ for the classical Kantorovich operators.